Ryan, I'm particularly interested in your opinion since you're doing most of the technical work on here, but it'd be good to get requests for any additional features. You might want to check out the most popular downloads, or search this forum to see if something specific exists - but keep in mind we presumably can't use mods for phpBB 2 versions.
The list of v3 mods might be more helpful, but you can't sort them.
(bear in mind we're using phpBB 3.0.2 at the moment - Ryan, there's info on updating that might mean more to you than me on the system tab on the admin panel - though it sounds as though we'll need the password reset to be able to proceed)
Browsing the phpBB forums list, the following seem good:
Simple Syndication - RSS and ATOM Webfeed syndicator - or Simple RSS mod for phpBB3 - Will enable you to put a RSS feed on your phpBB3 Forum.
Userfriendly URL-input while posting - makes inputting URLs easier, but it's designed for phpBB2. I haven't yet found anything similar for 3, and I presume 3's not backwards compatible...
YouTube video BB code - Adds a new bbcode allowing you to easily embed videos from YouTube.com. (again, version 2 though)
Prime Self Topics - Adds a "View your topics" link next to the "View your posts" link.
Welcome PM on First Login - Allows administrators to create a message that will be sent to newly registered users upon their first login. (How do people feel about getting these? I usually find them annoying, but I suppose if they gave a useful guide to the forum they might be worth considering... (but by the time people register, will they have already looked around the forum?)
Quick reply for phpBB3 - adds quick post form at viewforum and quick reply form at viewtopic, fully customizable from ACP/UCP. Allows quick quoting of selected text and quick nick insertion at viewtopic.
Last post titles - Displays the subject of LAST POST posted in a forum (I'm very keen on this one if I understand it right - I often get interested in a forum that I'm just passing through when I see a topic title that draws me)
Genders - allows your members to specify their Gender. They can chose between "Male", "Female" and "None specified".
NB - Ryan, we should postpone selecting a default skin/designing a logo until we've selected which mods we want to use, since some (all?) of them seem skin-dependent - usually on ProSilver.